Digital-to-analog conversion for audio applications is performed by generating the output analog signal as the sum, at each sampling instant, of a given number of elementary quantities or contributions, which may be, for example, currents supplied by elementary current generators or generated by means of resistors, or charges stored in capacitors. Digital-to-analog conversion can be roughly divided in two major categories according to the approach adopted in the conversion namely either “thermometric” or “binary” coding.
In thermometric coding, the elementary contributions used for generating the output analog signal assume values identical to one another and are generated by distinct sources numbering N, where N=2n represents the number of levels of the output analog signal for a number of bits equal to n. Optionally, in order to obtain a balanced output analog signal, i.e., an output signal of zero mean value, able to assume either positive values or negative values that are symmetrical with respect to zero, half (N/2) of the elementary sources may be designed for supplying positive elementary contributions and the other half of the sources for supplying negative elementary contributions to the output analog signal, and the value of each elementary contribution is 2AMAX/2n, where AMAX represents the maximum amplitude, either positive or negative, that the output analog signal should assume.
Differently, in binary coding, the number of distinct sources to be implemented for providing the elementary contributions is equal to the number of bits n of the digital-to-analog converter that is equal to n=log2N. The dimensions of the integrated elementary sources (for example current generators) are not identical but appropriately graded in such a way that the elementary contributions thereby produced are submultiples of a power of 2 with respect to the maximum value AMAX, in which the least significant bit (LSB) has a weight of 2AMAX/2n, whilst the most significant bit (MSB) has a weight of AMAX.
Usually, the numerical processing part of an audio DAC that precedes the analog output part, includes a numerical interpolator, followed by a noise shaping circuit, for the overall purpose of reducing the number of bits with which the digital PCM input signal is encoded, without worsening the quality in terms of in-band noise level.
More specifically, to maintain a high audio fidelity, the numerical interpolator performs an oversampling of the PCM signal, that is it increases the sampling frequency by a certain factor. This technique makes possible a reduction of the density in frequency of all spurious spectral components, eliminating undesired spectral repetitions.
The interpolation is followed by a noise-shaping operation including numerically differentiating the signal transfer function and the requantization error transfer function. By doing so, the input signal is transferred from the input to the output of the noise shaping circuit unaltered while the requantization error is subject instead to a transfer function typical of a high-pass filter, having a modulus smaller than one within the audio band and greater than one outside the audio band. The effect is of markedly increasing the precision even in presence of a quantizer with a very limited number of bits, even just one bit.
The numerical processing part of the digital-to-analog converter is then followed by a code conversion circuit that may be thought as representing (eventually in association to a scrambling circuit) the boundary between the digital and the analog domains of the converter. The code conversion circuit practically points to (selects) the elementary contributions to the analog output signal as a function of the digital code at its input.
Often, depending on the type of coding used, different techniques of dynamic element matching (DEM) may be optionally implemented to de-correlate the errors introduced by mismatchings among the graded current generators, in case of binary coding, or among the identical current generators, in the case of thermometric coding.
Numerous DEM techniques have been proposed for compensating the non-linearity of a DAC, the simplest being known in literature as “Randomization” or “Scrambling”. Accordingly, the elementary sources to be activated for producing respective contributions to the analog signal output by the DAC at every sampling period are chosen altogether at random among those available for selection, thus determining a variable error even in presence of a constant input value. On this basic approach, many more effective techniques have been developed.
Published U.S. Patent Application 2000/0063648A1, provides a review of numerous of these DEM techniques and discloses a method of dynamic matching of the elements of a multibit DAC with balanced output of audio applications.
Overall, the dynamic range remains a fundamental parameter of a digital to analog converter, representing the measure of the noise characteristic of the DAC circuit.
Typically, for an audio DAC, a −60 dB FS digital sine waveform is applied at the input and the ratio between the amplitude of the analog sine waveform reproduced at the output of the DAC and the amplitude of the residual noise plus the harmonics of the signal caused by the distortion introduced by the DAC plus 60 dB defines the dynamic range parameter (briefly DR), that isDR=20*LOG(Vsignal/V(noise+distorsion))+60 dB.
On another account, till recently the volume control was usually implemented in the analog part of the audio signal processing chain with traditional analog circuit components, that is downstream of the DAC in the signal path. It is more and more preferred by manufacturers of audio equipment, to implement the volume control in the digital domain, because of the augmented versatility to implement sophisticated automatic control and because of overall fabrication simplification, by no longer requiring external circuit components for analog volume control. Moreover, the elimination of an analog volume control makes possible the realization of the last functional blocks of a typical audio system, that is the audio DAC interface and the output power amplifier, on a single chip.
However, the choice of implementing the volume control in the digital signal processing part of the audio system, upstream of the DAC interface of the output power amplifier, has trade offs. Notably, the noise and distortion that are produced in the DAC are no longer attenuated by the analog volume control. In practice, in case of such “fully” digital systems, the output noise and distortion are generally higher than that of a comparable traditional system with analog volume control operating downstream of the DAC.
A measure of such a difference of output noise level for two comparable audio systems, 1) and 2), is illustrated in FIG. 1. The relatively higher output noise level of a system implementing a digital volume control in the digital signal processing portion of the chain of functional blocks of the system reduces proportionally the dynamic range.